Elliptic curve isogeny class 57.1-c over number field 4.4.19821.1

• Base field: 4.4.19821.1
• Label: 4.4.19821.1-57.1-c
• Conductor: 57.1
• Rank bounds: 0...1

Base field 4.4.19821.1

Generator \(a\), with minimal polynomial \( x^{4} - x^{3} - 8 x^{2} + 6 x + 3 \); class number \(1\).

Elliptic curves in class 57.1-c over 4.4.19821.1

Isogeny class 57.1-c contains only one elliptic curve.

Curve label	Weierstrass Coefficients
57.1-c1	\( \bigl[a^{2} - a - 4\) , \( -\frac{1}{3} a^{3} - \frac{1}{3} a^{2} + 3 a\) , \( a^{2} - a - 4\) , \( \frac{106}{3} a^{3} + \frac{10}{3} a^{2} - 278 a - 102\) , \( 883 a^{3} + 93 a^{2} - 6961 a - 2401\bigr] \)

Rank

Rank \(r\) satisfies \(0 \le r \le 1\)

Isogeny matrix

\(\left(\begin{array}{r} 1 \end{array}\right)\)

Isogeny graph